A curve approximation technique using quadratic B-splines is presented in this paper which automatically computes data points to minimize errors. This technique can be useful for efficient storage of geometric shapes in any graphic or CAD applications. The computed data points are the control points and knots of approximating quadratic B-spline curve rather than simple interpolants. Curve approximation is a three step process, involving computation of initial data points from the opening angle plot of given curve, new knot(s) insertion at appropriate location and error minimization by changing knot positions. The algorithm is simple, efficient and robust to any curve model. Demonstrated results show that even higher degree polynomial curves can be approximated with very few data points with reasonable accuracy.